EVALUATE THE POLYNOMIAL FOR THE GIVEN VALUES

Problem 1 :

Solve and verify your answer with these values

x = 1, y = -2

(13x + 7) (2y - 1)

Solution :

= (13x + 7) (2y - 1)

= 13x (2y - 1) + 7(2y - 1)

= 26xy - 13x + 14y - 7

By applying x = 1 and y = -2

= 26(1)(-2) - 13(1) + 14(-2) - 7

= -52 - 13 - 28 - 7

= - 100

Problem 2 :

Find the product of (3x - 7z) and (2y - 1) and evaluate for

x = 1, y = -2, z = 2

Solution :

= (3x - 7z) (2y - 1)

= 3x (2y - 1) - 7z (2y - 1)

= 6xy - 3x - 14yz + 7z

By applying x = 1, y = -2, z = 2

= 6(1)(-2) - 3(1) - 14(-2)(2) + 7(2)

= -12 - 3 + 56 + 14

= -15 + 70

= 55

Problem 3 :

Find the product of 

(1 + x² + y) (2x + z)

and evaluate for x = 1, y = 3, z = -2

Solution :

= (1 + x² + y) (2x + z)

= 1 (2x + z) + x² (2x + z) + y (2x + z)

= 2x + z + 2x³ + x²z + 2xy + yz

By applying x = 1, y = 3, z = -2

= 2(1) + (-2) + 2(1)³ + (1)²(-2) + 2(1)(3) + (3)(-2)

= 2 - 2 + 2 - 2 + 6 - 6

= 0

Problem 4 :

Find the product of 

(3x - 7z) and (2y - x - 1)

and evaluate for x = 0.1, y = -2.5, z = 2

Solution :

= (3x - 7z) (2y - x - 1)

= 3x (2y - x - 1) - 7z (2y - x - 1)

= 6xy - 3x² - 3x - 14yz + 7xz + 7z

By applying x = 0.1, y = -2.5, z = 2

= 6(0.1)(-2.5) - 3(0.1)² - 3(0.1) - 14(-2.5)(2) + 7(0.1)(2) + 7(2)

= -1.5 - 0.03 - 0.3 + 70 + 1.4 + 14

= -1.83 + 85.4

= 83.57